Various forms of communication links exhibit time-frequency spread which can make it difficult to recover a transmitted message so as to make available at the receiver a faithful reproduction of the message which has been transmitted. Examples of such media are HF links via the earth-ionispheric duct, underwater sonic and earth seismic links, troposcatter VHF links, and to some lesser extent, voice-quality telephone lines. Transmission difficulties are caused by a number of effects, such as multi-path reception, group delay distortion or, in general, time-spread of the time response of the overall transmission system. In addition, there also occurs Doppler, time-jitter, time-variable frequency offset or, in general, frequency spread of the overall response of the transmission system.
In order to overcome the undesirable waveform linear distortions that these effects introduce into the received form of a communicated message, the prior art has primarily processed the received signal in the time domain (see e.g., "Communication in Time Frequency-Spread Media Using Adaptive Equalization" by M. J. DiToro, found in the Proceedings of the IEEE, Volume 56, Number 10, October 1968, pages 1653-79). The ultimate goal of the prior art techniques, which is in common with the goal of this invention, is to provide at the receiver a reconstituted message which faithfully reproduces the message which was made available to the transmitter for transmission purposes. The present invention seeks, however, in distinction to the prior art, to achieve this result by processing the received message in the frequency domain rather than by operating on the received message in the time domain.
Therefore, it is one object of the present invention to provide a communication system in which the received message is processed, in the frequency domain, so as to provide a faithful reproduction of the message which was made available to the transmitter. It is another object of the invention to provide apparatus for use at a receiving station, for processing the received message in the frequency domain, so as to make available faithful reproductions of the message that was actually transmitted. It is still another object of the present invention to provide apparatus as is set forth above, which takes into account, in the processing, noise which may be received along with the message so that the ultimate reconstructed message made available is only to a small degree contaminated by noise.
If the transmission medium transfer function were known, the transmitted message could be reconstituted at the receiver by a de-convolution process since the received message is the convolution of the transmitted message and the transmission medium impulse response function. De-convolution in the time domain is difficult to achieve. However, in the frequency domain de-convolution is more tractable and is done simply by division wherein the transmitted message can be obtained by dividing the Fourier transform coefficients of the received message by the Fourier coefficients of the medium transfer function. This is a much more tractable problem.